Converting Percents to Fractions and Decimals

In this video lesson we're going to learn how to convert percents to fractions and decimals. And this skill is really important because when we're learning how to solve different problems that involve percent, we have to be able to convert it to a fraction or decimal before we calculate the problem.

So first we'll convert a percent to a fraction. And to do that we need to remove the percent sign. Then we're going to place that number as the numerator of the fraction and write 100 as the denominator. So if we want to write 27% as a fraction, first we'll remove the percent sign. We have just the number 27. That will be the numerator of the fraction. So it goes at the top and then we write 100 as the denominator and there's our fraction, 27 over 100. And if you think about it, it does make sense because percent means per 100. So 27% is the same as 27 per 100, or over 100.

Now let's see what happens when we convert a percent to a decimal. First we'll remove the percent sign and then we'll take that number and divide by 100. So if we start with 35% and we want to change it to a decimal, first we're going to remove the percent sign and then we'll divide by 100. But we'll need a little bit of workspace to do that. So let's set it up here.

So after we remove the percent sign we have just the number 35 and we'll divide it by 100. And we could write the division problem this way. But remember that a fraction can also represent division. So we could write it as 35 over 100, also to still show division but just as a fraction. So it doesn't matter which way you write it to start.

But to convert it to a decimal we will either have to do the division with a calculator or we can do long division and that's what we'll do here. So we have 35 divided by 100. One hundred can't go into 35. So we'll need to add some more digits after the 35.

And remember, whenever you have a whole number you can add a decimal point and a zero after it to make it into a decimal and it doesn't change the value of that number. So that still represents the number 35 but it gives us the extra digit that we need. And we'll also need to place a decimal point right above it where our quotient will be so that when we write the digits of our answer, we'll already have our decimal point lined up for us.

And once you do that you can go ahead and solve the problem and ignore the decimal point. So we'll treat this as 350 divided by 100. So 100 goes into 350 three times. 100 times three gives you 300, subtract that and we're left with 50. And we don't want to have a remainder here.

So we need to keep going, which means that we need another zero at the end of our 35 there. Bring down the zero. Now 100 goes into 500 five times. 100 times 5 is 500. Subtract that, and now we're left with no remainder. And that's what we want. So if we take a look up top our quotient, we have point 35. And we can put a zero in front to make it more complete. So now we can see that 35% as a decimal is zero point 35.

Now let's see what happens when we have percentages that are 100% or even higher than that. The two examples that we just saw involved percentages that were less than 100. But let's see what happens when we have exactly 100%. What will that look like as a fraction or decimal?

So 100% as a fraction would be 100 over 100. And if we simplify that, 100 divided by 100 is just equal to the whole number one. So it won't even give us a decimal. It gives us a whole number this time.

And what happens if we have something that's more than 100%? Like here, we have 329%. If we write that as a fraction, we can write it as 329 over 100. Or since this is an improper fraction, meaning that the numerator is larger than the denominator, we could write it as a mixed fraction, like this - three and 29 hundreds. And if we want to represent this as a decimal, it's going to be 3.29.

So if we have more than 100%, when we write it as a fraction or as a decimal, it's going to be more than one. So 100% will be equal to one. And if it's more than 100%, we'll get something that is more than one. So just keep that in mind as you are converting your percents to fractions and decimals.